Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Linear operators for which $ T\sp{\ast} T$ and $ TT\sp{\ast} $ commute

Author: Stephen L. Campbell
Journal: Proc. Amer. Math. Soc. 34 (1972), 177-180
MSC: Primary 47B99
MathSciNet review: 0295124
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Linear operators T for which $ {T^\ast}T$ and $ T{T^\ast}$ commute are studied. Examples are given to show that this class of operators is distinct from several other operator classes. It is proven that if $ {T^\ast}T$ and $ T{T^\ast}$ commute and T is hyponormal, then T has an invariant subspace. A generalization of this theorem is given.

References [Enhancements On Off] (What's this?)

  • [1] Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, With the assistance of William G. Bade and Robert G. Bartle, Interscience Publishers John Wiley & Sons New York-London, 1963. MR 0188745
  • [2] Peter A. Fillmore, Notes on operator theory, Van Nostrand Reinhold Mathematical Studies, No. 30, Van Nostrand Reinhold Co., New York-London-Melbourne, 1970. MR 0257765
  • [3] Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B99

Retrieve articles in all journals with MSC: 47B99

Additional Information

Keywords: Hyponormal operators, invariant subspaces, operators for which $ {T^\ast}T$ and $ T{T^\ast}$ commute
Article copyright: © Copyright 1972 American Mathematical Society